Search results for "68v20"
showing 7 items of 7 documents
About Graph Complements
2020
Summary This article formalizes different variants of the complement graph in the Mizar system [3], based on the formalization of graphs in [6].
Miscellaneous Graph Preliminaries
2020
Summary This article contains many auxiliary theorems which were missing in the Mizar Mathematical Library [2] to the best of the author’s knowledge. Most of them regard graph theory as formalized in the GLIB series (cf. [8]) and most of them are preliminaries needed in [7] or other forthcoming articles.
Miscellaneous Graph Preliminaries. Part I
2021
Summary This article contains many auxiliary theorems which were missing in the Mizar Mathematical Library to the best of the author’s knowledge. Most of them regard graph theory as formalized in the GLIB series and are needed in upcoming articles.
Extended Natural Numbers and Counters
2020
Summary This article introduces extended natural numbers, i.e. the set ℕ ∪ {+∞}, in Mizar [4], [3] and formalizes a way to list a cardinal numbers of cardinals. Both concepts have applications in graph theory.
Unification of Graphs and Relations in Mizar
2020
Summary A (di)graph without parallel edges can simply be represented by a binary relation of the vertices and on the other hand, any binary relation can be expressed as such a graph. In this article, this correspondence is formalized in the Mizar system [2], based on the formalization of graphs in [6] and relations in [11], [12]. Notably, a new definition of createGraph will be given, taking only a non empty set V and a binary relation E ⊆ V × V to create a (di)graph without parallel edges, which will provide to be very useful in future articles.
Refined Finiteness and Degree Properties in Graphs
2020
Summary In this article the finiteness of graphs is refined and the minimal and maximal degree of graphs are formalized in the Mizar system [3], based on the formalization of graphs in [4].
About Graph Unions and Intersections
2020
Summary In this article the union and intersection of a set of graphs are formalized in the Mizar system [5], based on the formalization of graphs in [7].